I think CX probably has the worst seat of the three, but the best service. I like the BA bed the best as you don't slide down it, unlike the QF bed. The BA one is completely flat, which is great for this side sleeper. The QF bed is still decent, but I'd take the BA bed any chance I can. That goes double for overnight sectors.
The average service on CX will be a notch above what QF & BA can offer from their best crews. They simply can't compete with CX here. With that said, I find sleep to be very important on LHR-HKG & vv sectors so I would probably shoot for BA. BA/QF have the best lounge in LHR, but CX has a fabulous lounge in HKG. Although if you have 1W elite status, you could use the CX lounge in HKG even if you fly BA/QF.